Problem: $ F = \left[\begin{array}{rr}2 & 2 \\ 1 & -2 \\ 0 & 0\end{array}\right]$ $ C = \left[\begin{array}{rr}4 & 0 \\ 3 & 3 \\ 0 & 3\end{array}\right]$ Is $ F- C$ defined?
Solution: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ F$ is of dimension $( m \times  n)$ and $ C$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ F$ ) must equal $ p$ (number of rows in $ C$ ) and 2. $ n$ (number of columns in $ F$ ) must equal $ q$ (number of columns in $ C$ Do $ F$ and $ C$ have the same number of rows? Yes Yes No Yes Do $ F$ and $ C$ have the same number of columns? Yes Yes No Yes Since $ F$ has the same dimensions $(3\times2)$ as $ C$ $(3\times2)$, $ F- C$ is defined.